(a) Determine a differential equation for the velocity v(t) of a mass m sinking in water that imparts a resistance proportional to the square of the instantaneous velocity (with a constant of proportionality k > 0) and also exerts an upward buoyant force whose magnitude is given by Archimedes' principle, which states that the upward buoyant force has magnitude equal to the weight of the water displaced. Assume that the positive direction is downward. (Let V be the volume of the object, e the weight density of water, and g the acceleration due to gravity.) dv g-k学+(-) e dt (b) Solve the differential equation in part (a). mg リー g k v(t) = e k (c) Determine the limiting, or terminal, velocity of the sinking mass. mg k lim v(t) =
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
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